# 2: Answer the above questions a,b,c,d,e, f,g for the system of linear equation
ID: 3116311 • Letter: #
Question
# 2: Answer the above questions a,b,c,d,e, f,g for the system of linear equations 4T1 822- lx3 + 9x4 + 1x5-13 1x1-2x2 +3x4 = 5 in the following manner: A) Write the augmented matrix B B) Write the equations in matrix form. That is as Ar = u with A the 3 by 5 matrix of coefficients of the unknowns x1 , T2, a, x4,T5, (1, T2, 23, x4, 5)t the column vector of unknowns. (13, 8,5)* the column vector of constants on the right. C) Go to www.wolfram.com and write the row reduced form of B C) Write all solutions using the reduced row form of B D) What is the dimension of the row space of B, that is the span of the rows? E) What is a basis for the row space of B? F) What is the dimension of the colurnn space of B, that is the span of the columns? G) What is a basis for the column space of B?Explanation / Answer
2. A).The augmented matrix for the given system of linear equations is B =
4
8
-1
9
1
13
1
2
1
6
-1
8
1
2
0
3
0
5
B).The given system of linear equations is represented in matrix form by BX = b, where B is as above, X = (x1,x2,x3,x4,x5)T and b = (13,8,5)T.
C). The RREF of B is
1
2
0
3
0
0
0
0
1
3
-1
0
0
0
0
0
0
1
D). As per the RREF of B, x1+2x2+3x4 = 0, x3+3x4-x5 = 0 and 0 =1.
E). A basis for the row space of B is{(1,2,0,3,0,0),(0,0,1,3,-1,0),(0,0,0,0,0,1)}.
F). & G).A basis for col(B) is { (1,0,0)T,(0,1,0)T, (0,0,1)T}.The dimension of col(B) is 3.
4
8
-1
9
1
13
1
2
1
6
-1
8
1
2
0
3
0
5
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